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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Bifurcation phenomena associated to the $ p$-Laplace operator


Authors: Mohammed Guedda and Laurent Véron
Journal: Trans. Amer. Math. Soc. 310 (1988), 419-431
MSC: Primary 35B32; Secondary 35J60
DOI: https://doi.org/10.1090/S0002-9947-1988-0965762-2
MathSciNet review: 965762
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Abstract: We determine the structure of the set of the solutions $ u$ of $ - {(\vert{u_x}{\vert^{p - 2}}{u_x})_x} + f(u) = \lambda \vert u{\vert^{p - 2}}u$ on $ (0,\,1)$ such that $ u(0) = u(1) = 0$, where $ p > 1$ and $ \lambda \in {\mathbf{R}}$. We prove that the solutions with $ k$ zeros are unique when $ 1 < p \leqslant 2$ but may not be so when $ p > 2$.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9947-1988-0965762-2
Article copyright: © Copyright 1988 American Mathematical Society

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